Quantum and classical complexity in coupled maps

TL;DR

This paper investigates the complexity growth in coupled quantum and classical maps with mixed dynamics, revealing differences in how quantum and classical measures capture complexity over time.

Contribution

It introduces a comparative analysis of quantum and classical complexity measures in coupled maps with different dynamical regimes, highlighting quantum-classical differences.

Findings

WSE and CSE grow similarly in hyperbolic cases.

WSE reaches high values faster in hyperbolic maps.

Classical features alone do not fully explain quantum complexity growth.

Abstract

We study a generic and paradigmatic two degrees of freedom system consisting of two coupled perturbed cat maps with different types of dynamics. The Wigner separability entropy (WSE) -- equivalent to the operator space entanglement entropy -- and the classical separability entropy (CSE) are used as measures of complexity. For the case where both degrees of freedom are hyperbolic, the maps are classically ergodic and the WSE and the CSE behave similarly, growing up to higher values than in the doubly elliptic case. However, when one map is elliptic and the other hyperbolic, the WSE reaches the same asymptotic value than that of the doubly hyperbolic case, but at a much slower rate. The CSE only follows the WSE for a few map steps, revealing that classical dynamical features are not enough to explain complexity growth.